Express this quotient in scientific notation: ${\frac{3.880\times 10^{3}} {4.0\times 10^{1}}}$
Answer: Start by collecting like terms together. $= {\frac{3.880} {4.0}} \times{\frac{10^{3}} {10^{1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.97 \times 10^{3\,-\,1}$ $= 0.97 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.97$ is the same as $9.70 \div 10$ , or $9.70 \times 10^{-1}$ $ = {9.70 \times 10^{-1}} \times 10^{2} $ $= 9.70\times 10^{1}$